Superhydrophobic behavior of a microtextured surface: a thermodynamic approach

A pillar microtexture, which has been intensively investigated in experiments, is chosen as a typical example and thermodynamically analyzed in detail. To gain a comprehensive insight into superhydrophobic behavior, the roles of pillar height, width and spacing (or roughness and solid fraction), intrinsic CA, drop size, and vibrational energy as well as fractal structure and formation of liquid films are systematically investigated. Solid surface fraction is shown by f. Free energy (FE) and free energy barrier (FEB) are calculated using a simple and robust 2D model. Based on the calculations of FE and FEB, various CAs, including apparent, equilibrium (stable), advancing and receding CAs, and CA hysteresis (CAH) can be determined. Especially, the design of practical surephydrophobic surfaces is emphasized in connection with the transition between noncomposite and composite states; a criterion for judging such transition is proposed. The theoretical results are consistent with Wenzel's and Cassie's equations and experimental observations. Furthermore, based on these results and the proposed criterion, some general principles to achieve superhydrophobic performance are suggested.